It is worth to mention that other concerns on these no-go theorems have already been pointed out [1]}, [2]}. In particular, only when a measurement is completed should a probability distribution be assigned. Assigning probability distribution for pre-measurement without result leads to contradiction [1]}. The analysis in this work will go one step further by showing that even assigning probability distribution for completed measurement, there is still logical loopholes in the no-go theorem. This is because the law of total probability that the proofs rely on does not hold true with the specific measurement operators and initial quantum state being chosen. Lastly, it is important to emphasize that we do not take a stand on the assertions of the no-go theorems themselves. For instance, it could be still a valid statement that “measured facts are observer-dependent”. What we show here is that there are logical loopholes in the proof of the no-go theorems.
